On the fine spectra of some averaging operators

The aim of this text is the study of the fine spectra for a class of Cesàro generalized operators, Rhaly operators, when those are defined on the spaces lp, p > 1. 2000 Mathematical Subject Classification: 65F15 The averaging operators A are determined by relations inf x∈X f(x) ≤ A(f) ≤ sup x∈X f(x) , ∀ f ∈ F = {f | f : X → R}, where ∅ 6= X ⊂ R. A(f) is the mean of f for the operator A. For a = (an) ∈ s, Rhaly operator Ra : s → s (Raf)(n) = an n ∑ i=0 f(i) , n ∈ N, for every f = (f(n))n∈N ∈ s = {g = (g(n))n∈N : g(n) ∈ C}.